Start Bayesian optimization before any experiments have been run — magp_bayes_optimize_from

Use this function when no initial data are available. It creates an initial quantitative-sequence design, evaluates FUN at those runs, and then uses MaGP expected improvement to select later runs.

Usage

magp_bayes_optimize_from_scratch(
  FUN,
  n_initial,
  q,
  model = c("2d", "full"),
  direction = c("minimize", "maximize"),
  n_iter = 10L,
  xi = 0,
  stop_ei = 0,
  stop_patience = 3L,
  seed = NULL,
  design_control = list(),
  fit_control = list(),
  acquisition_control = list(),
  objective_args = list(),
  verbose = TRUE
)

Arguments

FUN: Function that evaluates one experiment. It must accept the generated arguments quantity_1, ..., quantity_q, sequence_1, ..., sequence_q. It must return one finite number, or a list with one finite number named Score or Value.
n_initial: Number of experiments in the generated initial design.
q: Number of components. It must be at least three.
model: MaGP mapping to fit. Use "2d" for the compact mapping or "full" for the full mapping.
direction: Use "minimize" when smaller responses are better and "maximize" when larger responses are better.
n_iter: Maximum number of new experiments selected after the initial design has been evaluated.
xi: Nonnegative expected-improvement offset. The default, 0, uses the current best response as the improvement target.
stop_ei: Nonnegative early-stopping threshold for expected improvement.
stop_patience: Number of consecutive selected points with expected improvement less than or equal to stop_ei required to stop early.
seed: Optional nonnegative whole-number seed. It makes the initial design, model starts, acquisition searches, and random values produced by FUN reproducible while preserving the caller's random-number state.
design_control: Optional named list passed to magp_initial_design(). Use sequence_method to choose "random", "sfta", or "sann". Other common choices include sequence_maxit, sfta_control, quantity_maxit, and alignment_maxit. This function supplies n, q, and seed.
fit_control: Optional named list passed to magp2d_fit() or magpfull_fit(). Common choices are maxeval, n_starts, and workers. This function supplies X, y, and seed.
acquisition_control: Optional named list passed to magp_next_point(). Common choices are lower, upper, sequences, n_starts, workers, and maxit. This function supplies the fitted model, direction, xi, current best response, and seed.
objective_args: Optional named list of fixed arguments passed to FUN in addition to the generated input columns.
verbose: If TRUE, print one line after each initial and sequential evaluation.

Value

An object of class magp_bayes_opt containing the initial design, all completed evaluations, and the final fitted model.

How to use this function

Define FUN, choose n_initial and q, and state whether the response should be minimized or maximized. The function then:

creates an initial design;
calls FUN once for each initial row;
fits the selected MaGP model; and
selects and evaluates as many as n_iter additional rows.

The generated columns are named quantity_1 through quantity_q and sequence_1 through sequence_q. Use magp_bayes_optimize() instead when initial experiments and responses already exist.

Reading the result

The result has the same main components as magp_bayes_optimize(), including best_point, best_value, history, the final model, and all recorded search settings. It also contains:

initial_design: the generated quantitative-sequence design;
initial_response: the response from each initial run;
initial_evaluations: the number of initial runs; and
design_control: the initial-design settings that were used; and
started_from_initial_design: TRUE, marking that the workflow generated its own starting design.

Examples

# \donttest{
objective <- function(quantity_1, quantity_2, quantity_3,
                      sequence_1, sequence_2, sequence_3) {
  quantities <- c(quantity_1, quantity_2, quantity_3)
  sequence <- c(sequence_1, sequence_2, sequence_3)
  -sum((quantities - c(0.2, 0.6, 0.8))^2) -
    0.01 * sum((sequence - c(1, 3, 2))^2)
}
result <- magp_bayes_optimize_from_scratch(
  FUN = objective,
  n_initial = 6,
  q = 3,
  direction = "maximize",
  n_iter = 1,
  seed = 1,
  design_control = list(
    sequence_maxit = 100,
    quantity_maxit = 100,
    alignment_maxit = 100
  ),
  fit_control = list(maxeval = 100),
  acquisition_control = list(n_starts = 2, maxit = 20),
  verbose = FALSE
)
result$initial_design$design
#>      quantity_1 quantity_2 quantity_3 sequence_1 sequence_2 sequence_3
#> [1,] 0.75000000 0.08333333 0.25000000          1          2          3
#> [2,] 0.08333333 0.25000000 0.41666667          3          1          2
#> [3,] 0.25000000 0.58333333 0.91666667          2          1          3
#> [4,] 0.91666667 0.41666667 0.75000000          1          3          2
#> [5,] 0.41666667 0.75000000 0.08333333          2          3          1
#> [6,] 0.58333333 0.91666667 0.58333333          3          2          1
result$best_point
#> quantity_1 quantity_2 quantity_3 sequence_1 sequence_2 sequence_3 
#>  0.2500000  0.5833333  0.9166667  2.0000000  1.0000000  3.0000000 
result$best_value
#> [1] -0.07638889
result$history
#>   Iteration Initial quantity_1 quantity_2 quantity_3 sequence_1 sequence_2
#> 1         0    TRUE 0.75000000 0.08333333 0.25000000          1          2
#> 2         0    TRUE 0.08333333 0.25000000 0.41666667          3          1
#> 3         0    TRUE 0.25000000 0.58333333 0.91666667          2          1
#> 4         0    TRUE 0.91666667 0.41666667 0.75000000          1          3
#> 5         0    TRUE 0.41666667 0.75000000 0.08333333          2          3
#> 6         0    TRUE 0.58333333 0.91666667 0.58333333          3          2
#> 7         1   FALSE 0.00000000 0.00000000 1.00000000          1          3
#>   sequence_3       Value ExpectedImprovement PredictedMean
#> 1          3 -0.89194444                  NA            NA
#> 2          2 -0.36305556                  NA            NA
#> 3          3 -0.07638889                  NA            NA
#> 4          2 -0.54972222                  NA            NA
#> 5          1 -0.60305556                  NA            NA
#> 6          1 -0.35416667                  NA            NA
#> 7          2 -0.44000000            2.165427    -0.4700069
#>   PredictedStandardError
#> 1                     NA
#> 2                     NA
#> 3                     NA
#> 4                     NA
#> 5                     NA
#> 6                     NA
#> 7               5.908141
# }